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Abstract

In single particle imaging applications, the number of photons detected from the fluorescent label plays a crucial role in the quantitative analysis of the acquired data. For example, in tracking experiments the localization accuracy of the labeled entity can be improved by collecting more photons from the labeled entity. Here, we report the development of dual objective multifocal plane microscopy (dMUM) for single particle studies. The new microscope configuration uses two opposing objective lenses, where one of the objectives is in an inverted position and the other objective is in an upright position. We show that dMUM has a higher photon collection efficiency when compared to standard microscopes. We demonstrate that fluorescent labels can be localized with better accuracy in 2D and 3D when imaged through dMUM than when imaged through a standard microscope. Analytical tools are introduced to estimate the nanoprobe location from dMUM images and to characterize the accuracy with which they can be determined.

Figures (6)

Dual objective multifocal plane microscope. The figure shows a schematic of dMUM that is capable of imaging the sample from top and bottom. Our specific implementation of the dMUM imaging configuration used two inverted microscopes (Zeiss Ax-ioObserver), where one of the microscopes (top scope) was in an upside down orientation and mounted on linear translation stages that were then attached to the other microscope (bottom scope).

dMUM images of nanoprobe samples. Panels a and b show dMUM images of a 100 nm tetraspeck bead sample and a QD655 sample, respectively, and pertain to the 2D infocus imaging configuration. Panel c shows a dMUM image of a 100 nm tetraspeck bead sample that pertains to the 3D imaging configuration. This image was acquired by positioning the bottom scope objective close to the sample and the top scope objective a distance of 1.5μm away from the sample. In panel a (panel c) for the bead highlighted with an arrow, the number of photons detected in the bottom and top scope images are 4750 and 8770 (3600 and 5900), respectively. In panel b for the QD label highlighted with an arrow, the number of detected photons in the bottom scope and top scope images are 3100 and 8700, respectively. In all panels the rightmost column shows cropped images of the nanoprobe that are highlighted with an arrow in the left and center columns. The images shown are the raw data that are not spatially registered. Because of the use of different detectors to capture the images in the top and bottom scopes, there is a scale change between the bottom scope and top scope images. In all the panels, the nanoprobe images are numbered to aid visualization. Scale bar = 5μm.

Localization measure calculations for different microscope configurations. Panel a shows the variation of the 2D localization measure of x0/y0 coordinate as a function of the expected number of detected photons for dMUM (×,°) and for a standard microscope (*). Here, the photon detection rate for the standard microscope is set to 10,000 photons/s. For dMUM we consider two scenarios, one where we have the same photon detection rate of 10000 photons/s for the top and bottom scopes (×) and the other where we have different photon detection rates of 20000 photons/s and 10000 photon/s for the top and bottom scopes, respectively (°). The latter scenario of unequal photon detection rates occurs in our experimental data (Fig. 2). The following are the numerical values of the other parameters that are used to generate the plots in this panel: na = 1.2, M = 63, λ = 555 nm, the pixel array size is 11 × 11, the pixel size is 12.9 μm × 12.9 μm, the background component is 300 photons/pixel/s, the mean and standard deviation of the readout noise of the imaging detector are 0 e-/pixel and 8 e-/pixel, respectively, the X-Y coordinate of the nanoprobe is assumed to coincide with the center of the pixel array, and the noise statistics is assumed to be the same for all pixels. The x-axis range denotes the expected number of detected photons in the bottom scope which corresponds to an acquisition time range of 0.01 s to 1 s.

Schematic showing the 3D imaging configuration of dMUM and MUM. Both dMUM and MUM support simultaneous imaging of different focal planes. In dMUM the fluorescence signal is collected from above and below the sample by two different objective lenses, each of which is positioned such that they image a distinct focal plane. In MUM the fluorescence signal is detected from only one side of the sample. The collected signal is then split into two detectors, where each detector is placed at a specific calibrated distance from the tube lens.

Results of z-position estimation. The figure shows the z-position (z0) estimates from simulated images whose means and standard deviations are listed in Table 2. Panel a shows the z-position estimates from dMUM images and panel b shows the z-position estimates from MUM images. In both panels, (—) indicates the mean value of the z-position estimates.

Effect of focal plane spacing on the 3D localization measure of dMUM. The figure shows the variation of the 3D localization measure of z0 for dMUM as a function of the z-position for different plane spacing values of 1.0 μm (◇), 1.25 μm (*) and 1.5 μm (◁). All numerical values used to generate the above plots are identical to those used in Fig. 3(b).

Tables (2)

Table 1. Results of 2D location estimation from dMUM images. The table lists the standard deviation (std-dev) and the 2D localization measure (loc-meas) for the X/Y coordinate of 100 nm tetraspeck beads that were imaged in the 2D infocus imaging configuration. The X-Y estimates for dMUM were determined using the estimation algorithm described in Section 2.4. The X-Y estimates for the top and bottom scopes were independently determined by fitting Airy profiles to the corresponding images. All X-Y coordinates were drift corrected prior to calculating the standard deviation. For each nanoprobe sample, the standard deviation was calculated from 80 estimates. The 2D localization measure for each bead was computed as described in Section 2.6.

Table 2. Results of 3D location estimation from dMUM and MUM images. The table lists the z-position (z0), standard deviation (std-dev) of z-position estimates and the 3D localization measure (loc-meas) of z0 for dMUM/MUM. For each value of z0, 300 dMUM/MUM images were simulated and the z-position was estimated from these images using MUMLA (see section 2.5). Fig. 5 shows the plot of the z-position estimates for each z0 value for dMUM and MUM. The following numerical values were used to simulate the dMUM images. The wavelength of the detected photons was set to 525 nm, the numerical aperture and magnification of the bottom (top) scope objective were set to 1.2 and 63x (62.7x), respectively, the photon detection rate and background component for the bottom (top) scope were set to 3000 photon/s and 400 photons/pixel/s, respectively, the exposure time was set to 1 s, the pixel array size was set to 11 × 11, the pixel size was set to 12.9 μm×12.9 μm, the nanoprobe image was assumed to be at the center of the pixel array, the mean and standard deviation of the readout noise in the bottom (top) scope image were set to 0 e-/pixel and 8 e-/pixel (6 e-/pixel), respectively, and the plane spacing between the two focal planes was set to 1000 nm. The numerical values used to simulate the MUM images were identical to those used for simulating dMUM images, except that the photon detection rate and background component for the two focal planes were set to 1500 photon/s and 200 photons/pixel/s, respectively.

Metrics

Table 1.

Results of 2D location estimation from dMUM images. The table lists the standard deviation (std-dev) and the 2D localization measure (loc-meas) for the X/Y coordinate of 100 nm tetraspeck beads that were imaged in the 2D infocus imaging configuration. The X-Y estimates for dMUM were determined using the estimation algorithm described in Section 2.4. The X-Y estimates for the top and bottom scopes were independently determined by fitting Airy profiles to the corresponding images. All X-Y coordinates were drift corrected prior to calculating the standard deviation. For each nanoprobe sample, the standard deviation was calculated from 80 estimates. The 2D localization measure for each bead was computed as described in Section 2.6.

Bead #

Std-dev of x0, bottom scope [nm]

Std-dev of y0, bottom scope [nm]

Loc-meas of x0/y0, bottom scope [nm]

Std-dev of x0, top scope [nm]

Std-dev of y0, top scope [nm]

Loc-meas of x0/y0, top scope [nm]

Std-dev of x0, dMUM scope [nm]

Std-dev of y0, dMUM scope [nm]

Loc-meas of x0/y0, dMUM scope [nm]

1

4.8

4.3

4.5

5.4

5.4

5.7

3.8

3.3

3.5

2

4.4

3.8

4.2

5.8

5.4

5.7

3.5

3.4

3.4

3

4.0

3.5

3.4

4.5

5.5

4.2

3.0

2.7

2.6

4

4.3

3.9

4.1

5.5

5.4

5.1

3.3

3.1

3.2

Table 2.

Results of 3D location estimation from dMUM and MUM images. The table lists the z-position (z0), standard deviation (std-dev) of z-position estimates and the 3D localization measure (loc-meas) of z0 for dMUM/MUM. For each value of z0, 300 dMUM/MUM images were simulated and the z-position was estimated from these images using MUMLA (see section 2.5). Fig. 5 shows the plot of the z-position estimates for each z0 value for dMUM and MUM. The following numerical values were used to simulate the dMUM images. The wavelength of the detected photons was set to 525 nm, the numerical aperture and magnification of the bottom (top) scope objective were set to 1.2 and 63x (62.7x), respectively, the photon detection rate and background component for the bottom (top) scope were set to 3000 photon/s and 400 photons/pixel/s, respectively, the exposure time was set to 1 s, the pixel array size was set to 11 × 11, the pixel size was set to 12.9 μm×12.9 μm, the nanoprobe image was assumed to be at the center of the pixel array, the mean and standard deviation of the readout noise in the bottom (top) scope image were set to 0 e-/pixel and 8 e-/pixel (6 e-/pixel), respectively, and the plane spacing between the two focal planes was set to 1000 nm. The numerical values used to simulate the MUM images were identical to those used for simulating dMUM images, except that the photon detection rate and background component for the two focal planes were set to 1500 photon/s and 200 photons/pixel/s, respectively.

Defocus level

True value of z0 [nm]

Std-dev of z0 DMUM [nm]

3D loc-meas of z0 DMUM [nm]

Std-dev of z0 MUM [nm]

3D loc-meas of z0 MUM [nm]

1

-1200

36

36

51

54

2

-900

30

29

42

43

3

-600

16

15

23

22

4

-300

21

19

28

28

5

0

23

29

40

40

6

300

13

11

17

17

7

600

10

10

14

14

8

900

21

22

33

33

9

1200

23

23

33

33

Tables (2)

Table 1.

Results of 2D location estimation from dMUM images. The table lists the standard deviation (std-dev) and the 2D localization measure (loc-meas) for the X/Y coordinate of 100 nm tetraspeck beads that were imaged in the 2D infocus imaging configuration. The X-Y estimates for dMUM were determined using the estimation algorithm described in Section 2.4. The X-Y estimates for the top and bottom scopes were independently determined by fitting Airy profiles to the corresponding images. All X-Y coordinates were drift corrected prior to calculating the standard deviation. For each nanoprobe sample, the standard deviation was calculated from 80 estimates. The 2D localization measure for each bead was computed as described in Section 2.6.

Bead #

Std-dev of x0, bottom scope [nm]

Std-dev of y0, bottom scope [nm]

Loc-meas of x0/y0, bottom scope [nm]

Std-dev of x0, top scope [nm]

Std-dev of y0, top scope [nm]

Loc-meas of x0/y0, top scope [nm]

Std-dev of x0, dMUM scope [nm]

Std-dev of y0, dMUM scope [nm]

Loc-meas of x0/y0, dMUM scope [nm]

1

4.8

4.3

4.5

5.4

5.4

5.7

3.8

3.3

3.5

2

4.4

3.8

4.2

5.8

5.4

5.7

3.5

3.4

3.4

3

4.0

3.5

3.4

4.5

5.5

4.2

3.0

2.7

2.6

4

4.3

3.9

4.1

5.5

5.4

5.1

3.3

3.1

3.2

Table 2.

Results of 3D location estimation from dMUM and MUM images. The table lists the z-position (z0), standard deviation (std-dev) of z-position estimates and the 3D localization measure (loc-meas) of z0 for dMUM/MUM. For each value of z0, 300 dMUM/MUM images were simulated and the z-position was estimated from these images using MUMLA (see section 2.5). Fig. 5 shows the plot of the z-position estimates for each z0 value for dMUM and MUM. The following numerical values were used to simulate the dMUM images. The wavelength of the detected photons was set to 525 nm, the numerical aperture and magnification of the bottom (top) scope objective were set to 1.2 and 63x (62.7x), respectively, the photon detection rate and background component for the bottom (top) scope were set to 3000 photon/s and 400 photons/pixel/s, respectively, the exposure time was set to 1 s, the pixel array size was set to 11 × 11, the pixel size was set to 12.9 μm×12.9 μm, the nanoprobe image was assumed to be at the center of the pixel array, the mean and standard deviation of the readout noise in the bottom (top) scope image were set to 0 e-/pixel and 8 e-/pixel (6 e-/pixel), respectively, and the plane spacing between the two focal planes was set to 1000 nm. The numerical values used to simulate the MUM images were identical to those used for simulating dMUM images, except that the photon detection rate and background component for the two focal planes were set to 1500 photon/s and 200 photons/pixel/s, respectively.